The Slicing Problem by Bourgain

B. Klartag () and V. Milman ()
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B. Klartag: Department of Mathematics, Weizmann Institute of Science
V. Milman: Tel Aviv University, School of Mathematical Sciences

A chapter in Analysis at Large, 2022, pp 203-231 from Springer

Abstract: Abstract In the context of his work on maximal functions in the 1980s, Jean Bourgain came across the following geometric question: Is there c > 0 such that for any dimension n and any convex body K ⊆ ℝ n $$K \subseteq \mathbb R^n$$ of volume one, there exists a hyperplane H such that the (n − 1)-dimensional volume of K ∩ H is at least c? This innocent and seemingly obvious question (which remains unanswered!) has established a new direction in high-dimensional geometry. It has emerged as an “engine” that inspired the discovery of many deep results and unexpected connections. Here we provide a survey of these developments, including many of Bourgain’s results.

Date: 2022
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DOI: 10.1007/978-3-031-05331-3_9

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